Advances in the numerical treatment of grain-boundary migration: Coupling with mass transport and mechanics

Mourad, Hashem M.; Garikipati, Krishna

doi:10.1016/j.cma.2006.06.005

Cited by 21 publications

(17 citation statements)

References 43 publications

(70 reference statements)

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“…74,75 The interactions of vacancies and grain boundaries are of great importance to understanding void formation in ICs. 76 Void formation has been attributed to the coalescence of vacancies along grain boundaries.…”

Section: Discussionmentioning

confidence: 99%

Stress-Induced Grain Boundary Migration in Polycrystalline Copper

Bloomfield

Bentz

Cale

2007

Journal of Elec Materi

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We use three-dimensional (3D) grain-continuum models to study grain boundary migration, treating each grain with anisotropic elastic properties. Grain boundary speeds are computed using a finite element method to calculate differences in strain energy density across grain boundaries. Bodyfitted finite element meshes are used. An interface tracking program, PLENTE, is used to develop starting structures and move the grain boundaries based on these speeds. We demonstrate this procedure on textured films consisting of h100i and h111i fiber textured film. We also apply the model to a short section of a Cu line embedded in oxide. We conclude with a discussion on the relative impact of different driving forces for grain boundary motion.

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Section: Discussionmentioning

confidence: 99%

Stress-Induced Grain Boundary Migration in Polycrystalline Copper

Bloomfield

Bentz

Cale

2007

Journal of Elec Materi

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“…The level set equation is typically solved on rectangular grids, which may be a limitation for simulation of general complex structures. However, some works have been recently published where the level set method is implemented for unstructured triangulated meshes in connection to mass transport and mechanics [105][106][107].…”

Section: Level Set Methodsmentioning

confidence: 99%

Physically based models of electromigration: From Black’s equation to modern TCAD models

Orio

Ceric

Selberherr

2010

Microelectronics Reliability

118

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“…Work has been done on atomic migration, particularly along grain boundaries [12][13][14] and in the presence of electrical currents [15][16][17]. (A reasonable review of work in this area is beyond the scope of this paper.)…”

Section: Stress Induced Vacancy Migrationmentioning

confidence: 99%

Influences of grain structure on thermally induced stresses in 3D IC inter-wafer vias

et al. 2006

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We discuss the development of a grain-continuum model to examine the effects of thermally induced stress in 3D IC inter-wafer vias. We demonstrate the approach using stress-driven grain boundary migration in polycrystalline copper films, assuming that migration is due to vacancy migration. The anisotropic elastic constants of single crystal Cu are used for each grain, after aligning them with each grain's orientation. Stresses are thermally induced in a series of films, including one with a dominant <111> texture surrounding a single <100> grain. Grain boundary velocities are calculated from the fluxes of vacancies to grain boundaries. The computed velocities are then used to update the level sets that represent the grain boundaries using the PLENTE software.We present the status of our thermo-mechanical modeling effort to provide parameters for the design and fabrication of 3D ICs based on benzocylcobutene (BCB) wafer bonding [1]. Broadly speaking, the stability concerns for inter-wafer Cu vias in 3D ICs are extensions of those for Cu-based MLM structures. For 3D ICs, a major reliability concern is the stability of the vias, which pass through several materials/layers.We have used Comsol Multiphysics (CM) [2] in thermomechanical modeling of inter-wafer Cu vias. Using structures such as the one displayed in Fig. 1a, we treated Cu as a homogenous material placed under stress from CTE mismatches with surrounding materials. We concluded that the inter-wafer vias are susceptible to failure, depending on the BCB thickness, via pitch, and via diameter. The impact of grain structure on these systems was introduced via a HallPetch correlation of the Cu yield stress with grain size. We validated our approach by comparing our results to data from reliability studies of Cu via structures in SiCOH and SiLK [3,4], as well as XRD studies of damascene-patterned Cu lines [5]. Since these results indicate that stresses are a potential reliability issue, we are extending our model in order to improve on our predicted design parameters and examine the types of potential failures.Because the smallest dimensions of the structures in question are on the same length scale as the grains within the Cu, the granular nature of the Cu may have a significant effect on the mechanical response of the system [6]. Moreover, the homogeneous isotropic results show large gradients in the stresses, which may provide driving forces for grain structure evolution. We report on efforts to include polycrystallinity into thermal mechanical models and to consider the effects of anisotropy and potential grain structure evolution. To include such crystallinitiy, we formulate 'grain-continuum' models, in which each grain is treated as a continuum, while grain boundaries are separately represented [7]. Effects of elastic anisotropyCu grains are anisotropic. The elastic modulus for single crystal Cu is 2.9 times larger in the <111> direction and 2.0 times larger in the <110> than it is in the <100> direction Springer

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Advances in the numerical treatment of grain-boundary migration: Coupling with mass transport and mechanics

Cited by 21 publications

References 43 publications

Stress-Induced Grain Boundary Migration in Polycrystalline Copper

Stress-Induced Grain Boundary Migration in Polycrystalline Copper

Physically based models of electromigration: From Black’s equation to modern TCAD models

Influences of grain structure on thermally induced stresses in 3D IC inter-wafer vias

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